(countable) A statement that contradicts itself, i.e., a statement that makes a claim that the same thing is true and that it is false at the same time and in the same senses of the terms.

There is a contradiction in Clarence Page's statement that a woman should have the right to choose and decide for herself whether to have an abortion, and at the same time she should not have that right.

There is a contradiction in what you say - she can't be both married and single.

(countable) a logical incompatibility among two or more elements or propositions

Marx believed that the contradictions of capitalism would lead to socialism.